In this study, a fine local modeling of the coupled heat and mass transfer during absorption process of water vapor by a LiBr solution in a spiral tubular absorber of an absorption chiller was made. We have taken into account of the real hydrodynamics of the liquid solution that reveals the presence of three different flow regimes: a falling film region existing on the tube in which circulates the cooling water, a droplet formation region at the tube's bottoms and a droplet free fall region between the spaced tubes. The equations governing the coupled heat and mass transfer are established for the three flow regimes. The numerical simulation has given the distributions of different absorption parameters along the absorber tubes. This numerical simulation has shown up the relationship between the heat and the mass transfers and also highlighted the importance of the droplet formation and fall regimes in improving the absorption process, when the droplets are considered fully mixed. The validity of the model was improved using experimental data performed on a spiral tubular absorber of a double effect absorption chiller.